where \(c(\cdot )\)  is a consumption process serving as the control. Indeed, (REF ) is a general form of the SDU in Duffie–Epstein [1]}, involving the delay.
The goal of the optimal control problem is to find an optimal control process \(\tilde{v}\in {\cal U}\)  to maximize the cost functional (REF ) for given \((t,\gamma )\) .
